THREE:It has been already shown how Extension, having become identified with matter, took on its mechanical qualities, and was conceived as a connected series of causes or modes of motion. The parallel found by Spinoza for this series in Thought is the chain of reasons and consequents forming a410 demonstrative argument; and here he is obviously following Aristotle, who although ostensibly distinguishing between formal and efficient causes, hopelessly confounds them in the second book of his Posterior Analytics.565 We are said to understand a thing when we bring it under a general rule, and also when we discover the mechanical agency which produces it. For instance, we may know that a particular man will die, either from the fact that all men are mortal, or from the fact that he has received a fatal wound. The general rule, however, is not the cause of what will happen, but only the cause of our knowing that it will happen; and knowledge of the rule by no means carries with it a knowledge of the efficient cause; as we see in the case of gravitation and other natural forces whose modus operandi is still a complete mystery. What deceived Aristotle was partly his false analysis of the syllogism, which he interpreted as the connexion of two terms by the interposition of a middle answering to the causal nexus of two phenomena; and partly his conception of the universe as a series of concentric spheres, through which movement is transmitted from without, thus combining the two ideas of notional comprehension and mechanical causation."Very well, sir."
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THREE:Thus, so far as was possible in such altered circumstances, did the Renaissance of the second century reproduce the271 intellectual environment from which Platos philosophy had sprung. In literature, there was the same attention to words rather than to things; sometimes taking the form of exact scholarship, after the manner of Prodicus; sometimes of loose and superficial declamation, after the manner of Gorgias. There was the naturalism of Hippias, elaborated into a system by the Stoics, and practised as a life by the new Cynics. There was the hedonism of Aristippus, inculcated under a diluted form by the Epicureans. There was the old Ionian materialism, professed by Stoics and Epicureans alike. There was the scepticism of Protagoras, revived by Aenesidmus and his followers. There was the mathematical mysticism of the Pythagoreans, flourishing in Egypt instead of in southern Italy. There was the purer geometry of the Alexandrian Museum, corresponding to the school of Cyrn. On all sides, there was a mass of vague moral preaching, without any attempt to exhibit the moral truths which we empirically know as part of a comprehensive metaphysical philosophy. And, lastly, there was an immense undefined religious movement, ranging from theologies which taught the spirituality of God and of the human soul, down to the most irrational and abject superstition. We saw in the last chapter how, corresponding to this environment, there was a revived Platonism, that Platonism was in fact the fashionable philosophy of that age, just as it afterwards became the fashionable philosophy of another Renaissance thirteen centuries later. But it was a Platonism with the backbone of the system taken out. Platos thoughts all centred in a carefully considered scheme for the moral and political regeneration of society. Now, with the destruction of Greek independence, and the absorption everywhere of free city-states into a vast military empire, it might seem as if the realisation of such a scheme had become altogether impracticable. The Republic was, indeed, at that moment realising itself under a form adapted to the altered exigencies of the time; but no Platonist could as yet recognise272 in the Christian Church even an approximate fulfilment of his masters dream. Failing any practical issue, there remained the speculative side of Platos teaching. His writings did not embody a complete system, but they offered the materials whence a system could be framed. Here the choice lay between two possible lines of construction; and each had, in fact, been already attempted by his own immediate disciples. One was the Pythagorean method of the Old Academy, what Aristotle contemptuously called the conversion of philosophy into mathematics. We saw in the last chapter how the revived Platonism of the first and second centuries entered once more on the same perilous path, a path which led farther and farther away from the true principles of Greek thought, and of Plato himself when his intellect stood at its highest point of splendour. Neo-Pythagorean mysticism meant an unreconciled dualism of spirit and matter; and as the ultimate consequence of that dualism, it meant the substitution of magical incantations and ceremonial observances for the study of reason and virtue. Moreover, it readily allied itself with Oriental beliefs, which meant a negation of natural law that the Greeks could hardly tolerate, and, under the form of Gnostic pessimism, a belief in the inherent depravity of Nature that they could not tolerate at all.
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THREE:No computations, drawings, or demonstrations of any kind will be employed to relieve the mind of the reader from the care of remembering and a dependence on his own exertions. Drawings, constants, formul?, tables, rules, with all that pertains to computation in mechanics, are already furnished in many excellent books, which leave nothing to be added, and such books can be studied at the same time with what is presented here.
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